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8. CW-NR Bloch[]Z (longitudinal relaxation timexy (transversal relaxation timebloembergen [] Bloch Bloembergen Bloch (3.. d d d x z = ( ω ω = ωz + ( ω ω x = ω ( z x (8..a (8..b (8..c = z = z θ = ω t ( ω θ = ω θ = ω ω = (8.. ω dx x = (8..3a dθ θ d = z+ x (8..3b dθ θ dz ( z = (8..3c dθ θ

8. CW-NR 95 x θ ( ω ω ω = = + θ + θθ + {( ω ω } + ω θ ω = = + θ + θθ + {( ω ω } + ω + θ + {( ω ω } = = + θ + θθ + {( ω ω } + ω z (8..a (8..b (8..c BX = B cosωt X Y = cosωt sinωt X x = sinωt+ cosωt Y x mh mh cosω ( ω ω ω χ ω χ X = t+ sinωt + {( ω ω } + ω + {( ω ω } + ω χ m (.. = χ H cosωt+ χ H sinωt (8..5 X χ χ χ = χ iχ ( ω ω ω χ = χm (8..6a + ({ ω ω } + ω ω χ = χm (8..6b + ({ ω ω } + ω dbx P = X = χ HBω + ω δ = 8.

96 8. χ χ χ χ CWcontinuous wave NR (8..cZω= ω ( + ω = = sec /=Hz.5 (8..6ω ω ωχm ( χ χ + ω + ω χ ω χ ( ( + m m ω + ω = (8..7 ω ( χ, χ 8. ωχ m + ω ωχ m + ω ωχm (, χ + ω

8. CW-NR 97 χ ωχ m χ = (8..8a + max ω χ = max ωχm + ω (8..8b ω χ χ χ 8. χ χ t = (8.. d x d d z = x = ωz = ω ( z x (8..9a (8..9b (8..9c

98 d = z (8..a dθ θ dz ( z = (8..b dθ θ ( z z / θ =, = 8. 3 θ 8. 3 z / θ = ( z θ = 8. NRBloch []Bloembergen [] Kubo omita[3] BPPSolomon [] Kubo-omitaRedfield

8. 99 [5]Redfield Kubo-omita-Redfield / αβ 8. n n W β 8. αβ n n ( α W α β ( β α dn α dn β = W n + W n ( α β α ( β α β = W n W n ( α β α ( β α β (8.. ( αβ W( β α W α β dn dn α β = = W W ( α β β W( α β = exp( γ B / k = W α ( β α n n W ( β α (8..

W W ( α β ( β α γ B = W( k γ B = W( + k n = n n α β dn = W( n neq (8.. = W (8..5 W BloembergenSolomon 8. 3 H H (t[5,6]h (t d ρ = [ H (, i t ρ ] (8.3. iht iht ρ = exp( ρexp( iht iht H = exp( H( texp( (8.3. t ρ( t = ρ( + [ H ( t, ρ( t ] (8.3.3 i ρ ( t ρ ( t = ρ ( + [ H ( t,{ ( [ H ( t, ( t ]}] i ρ + ρ (8.3. t t ih d ρ = [ H ( t, ρ (] + ( [ H ( t,[ H ( t, ( t ]] (8.3.5 i i t ρ

8. 3 H ( t = H (tρ( t t t = t τ τ d ρ t = dτ[ H( t,[ H( t τ, ρ ( t τ ]] (8.3.6 H (th (t-τττ τ t τ ρ ( t τ ρ ( t c d ρ = dτ[ H( t,[ H( t τ, ρ ( t] ] (8.3.7 ρ H (t G αα ββ G = H t H t (8.3.8 αα, ββ ( τ ( α ( α ( β ( τ β, ( τ τ j i j, ( G, ( e ωτ αα ββ ω αα ββ τ d d ρ = τ (8.3.9 i( α α β+ β t αα t = Rαα, ββ e ρββ ββ ( ( t (8.3. αα α R αα, ββ R αα, ββ = { j αβ, αβ ( α β + j αβ, αβ ( β α δβα j γβ, γα ( γ β δβα j βγ, αγ ( β γ} γ γ c (8.3. β β = α α (8.3.

d ρ αα t = Rαα, ββ ββ ββ ( ' ρ ( t (8.3.3 (8.3. d ρ αα t = Rαα, ββ ββ β ( ' ρ ( t (8.3. ρ αα, ββρββ Rββαα, ραα R αα = (8.3.5 R, = R, (8.3.6 ρ αα ββ ββ ραα ββ αα = (8.3.7 (8.3. ρ ( ρ ( t ββ ββ ρβ β ρ Eβ k e ββ = δββ Eγ k e γ (8.3.8 d ρ ( = ' ( ρ ( ρ (8.3.9 αα t Rαα, ββ ββ t ββ ββ master equationρ (8.3.(8.3.3 d i ρ ( [, ρ(] ' ( ρ ( ρ (8.3. αα t = H t αα + Rαα, ββ ββ t ββ ββ

8. 3 8. A q= q ( q ( q H ( t = ( A ( t (8.. A ( q q ( q = ( A (8.. ( q + q ( q = ( (8..3 H q ( q ( q i ( t e α α = q ( α H α ( A ( t( α α ( q iht iht ( q ( q ( q i p t ( q ( = p, ωp = ω p p e e e ω q (8.. ( ( ( ( ( ( q q q q iw p t = p q p H t A t e (8..5 ( q ( q q ( q ( q q ( q τ δq q τ δq q A ( t A ( t+ = ( A ( t A ( t+ = ( c ( τ (8..6 (8..5(8.3.7 ρ ( ρ ( t ρ β d ρ p, ( q ( q q ( q p q p, ββ ββ β ( q iw '[,[,( ( t ]] ( c ( e p τ = ρ ρ τ dτ (8..7 ( q ( q p ' ωp + ω = ( q ( q iωτ J ( ω = c ( τ e dτ (8..8

( q ( q i j ( ω = c ( τ e ωτ dτ (8..9 k ( q ( q ( ω = c sin( ωτ dτ (8.. ( ( ( j q ( ω = J q ( ω ik q ( ω d ρ q ( q ( q ( q ( q ( q ( q = '( [,[,( ( p ρ t ρ ]]{ J ( ωp ik ( ωp } (8.. q p, d ρ q ( q ( q ( q ( q = '( J ( ω [,[,( ( p p ρ t ρ ]] (8.. q p, B < B > = r{ ρ B} r{[ A,[ B, C]] D} = r{ C[ B,[ A, D]]} (8..3 (8.. (8.. B d ρ q ( q ( q ( q ( q r B = r{ '( J ( ω [,[,( ( p p ρ t ρ ]] B} (8..5 q p, d < B > = q ( q ( q ( q ( q r{( ρ ( t ρ '( ( [,[, ]]} J ωp p B q p, q ( q ( q ( q ( q b = '( J ( ω [,[, ]] p p B q p, (8..6 (8..7 < b > = r{ ρ b} (8..8a b = r{ ρ b} (8..8b d < B > = < ( b > b (8..9 BI Z z

5 F. Bloch, Phs. Rev. 7, 6(96. N. Bloembergen, E.. Purcell, and R. V. Pound, Phs. Rev. 73, 679(98. 3 R. Kubo and K. omita, J. Phs. Soc. Jpn. 9, 888(95. I. Solomon, Phs. Rev. 99, 559(955. 5 A. C. Redfield, IB J. Res. Develop., 9(957. 6 A. Abragam, he Principles of Nuclear agnetism, Clarendon Press, Oxford, 963. 96

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